Answer to Question #113730 in Statistics and Probability for Katenda

Question

QUESTIONS 9 TO 11 ARE BASED ON THE FOLLOWING INFORMATION.

A practicing statistician wants to test the following hypothesis at a 5% level of significance:

H0 : π = 0.25
H1 : π ≠ 0.25

From a sample of 100, p = 0.22

Question 9

What is the value of the test statistic?

(1) 0.72
(2) 0.72
(3) 0.69
(4) 0.69
(5) 1.44

Question 10

What is the p-value of the test?

(1) 0.4906
(2) 0.4716
(3) 0.2451
(4) 0.2358
(5) p-value < 0.002

Question 11

Consider the following decisions and reasons with regard to the practicing Statistician’s hypothesis test.

(A) Reject the null hypothesis because p-value < a
(B) Reject the null hypothesis because |Z| > |Za/2|
(C) Do not reject the null hypothesis because p-value > a.
(D) Do not reject the null hypothesis because |Z| < |Za/2|

Which of the above statements are correct?

(1) A only.
(2) C Only.
(3) A and B only.
(4) C and D only.
(5) A, B and C only.

Answer 1

Question 9

What is the value of the test statistic? 

$$z={p-\pi \over \sqrt{\pi(1-\pi)n}}={0.22-0.25 \over \sqrt{0.25(1-0.25)100}}\approx-0.6928$$

$-0.69$

Question 10

What is the p-value of the test? 

The p-value is $0.4906$

Question 11

Consider the following decisions and reasons with regard to the practicing Statistician’s hypothesis test.

(A) Reject the null hypothesis because p-value < a

(B) Reject the null hypothesis because |Z| > |Za/2|

(C) Do not reject the null hypothesis because p-value > a.

(D) Do not reject the null hypothesis because |Z| < |Za/2|

Which of the above statements are correct? 

The p-value is $0.4906,$ and since $0.4906>0.05,$ it is concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than $\pi,$ at the $\alpha=0.05$ significance level.

(C) Do not reject the null hypothesis because p-value > $\alpha$